The LLV decomposition of hyper-Kähler cohomology (the known cases and the general conjectural behavior)
Abstract Looijenga–Lunts and Verbitsky showed that the cohomology of a compact hyper-
Kähler manifold X admits a natural action by the Lie algebra so (4, b_2 (X)-2) so (4, b 2 (X) …
Kähler manifold X admits a natural action by the Lie algebra so (4, b_2 (X)-2) so (4, b 2 (X) …
Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type
Given a smooth projective variety, a Chow–Künneth decomposition is called multiplicative if
it is compatible with the intersection product. Following works of Beauville and Voisin, Shen …
it is compatible with the intersection product. Following works of Beauville and Voisin, Shen …
Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
G Oberdieck - Geometry & Topology, 2024 - msp.org
We conjecture that the generating series of Gromov–Witten invariants of the Hilbert schemes
of n points on a K3 surface are quasi-Jacobi forms and satisfy a holomorphic anomaly …
of n points on a K3 surface are quasi-Jacobi forms and satisfy a holomorphic anomaly …
Gopakumar–Vafa type invariants of holomorphic symplectic 4-folds
Y Cao, G Oberdieck, Y Toda - Communications in Mathematical Physics, 2024 - Springer
Abstract Using reduced Gromov–Witten theory, we define new invariants which capture the
enumerative geometry of curves on holomorphic symplectic 4-folds. The invariants are …
enumerative geometry of curves on holomorphic symplectic 4-folds. The invariants are …
Multiple cover formulas for K3 geometries, wall-crossing, and Quot schemes
G Oberdieck - arXiv preprint arXiv:2111.11239, 2021 - arxiv.org
Let $ S $ be a K3 surface. We study the reduced Donaldson-Thomas theory of the cap
$(S\times\mathbb {P}^ 1)/S_ {\infty} $ by a second cosection argument. We obtain four main …
$(S\times\mathbb {P}^ 1)/S_ {\infty} $ by a second cosection argument. We obtain four main …
The LLV decomposition of hyper-Kähler cohomology
Looijenga--Lunts and Verbitsky showed that the cohomology of a compact hyper-K\" ahler
manifold $ X $ admits a natural action by the Lie algebra $\mathfrak {so}(4, b_2 (X)-2) …
manifold $ X $ admits a natural action by the Lie algebra $\mathfrak {so}(4, b_2 (X)-2) …
Algebraic cycles and Fano threefolds of genus 8
R Laterveer - preprint, 2021 - ems.press
PM_78_3-4_01_Laterveer 255..280 Page 1 Portugal. Math. (NS) 6 2022 Sociedade Portuguesa
de Matem·tica Vol. 78, Fasc. 3/4, 2021, 255–280 Published by EMS Press DOI 10.4171/PM/2069 …
de Matem·tica Vol. 78, Fasc. 3/4, 2021, 255–280 Published by EMS Press DOI 10.4171/PM/2069 …
On generalized Beauville decompositions
Y Bae, D Maulik, J Shen, Q Yin - arXiv preprint arXiv:2402.08861, 2024 - arxiv.org
Motivated by the Beauville decomposition of an abelian scheme and the" Perverse= Chern"
phenomenon for a compactified Jacobian fibration, we study in this paper splittings of the …
phenomenon for a compactified Jacobian fibration, we study in this paper splittings of the …
Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-K\" ahler manifolds
G Oberdieck, J Song, C Voisin - arXiv preprint arXiv:2110.02211, 2021 - arxiv.org
We prove that the complex cobordism class of any hyper-K\"{a} hler manifold of dimension
$2 n $ is a unique combination with rational coefficients of classes of products of punctual …
$2 n $ is a unique combination with rational coefficients of classes of products of punctual …
Bloch's conjecture for (anti-) autoequivalences on K3 surfaces
In this paper, we study Bloch's conjecture for zero cycles on K3 surfaces and hyper-K\" ahler
varieties. We prove Bloch's conjecture for reflexive autoequivalences on K3 surfaces. This …
varieties. We prove Bloch's conjecture for reflexive autoequivalences on K3 surfaces. This …